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A261962

Number of compositions of n such that no part equals any of its two immediate predecessors.

1, 1, 1, 3, 3, 5, 11, 15, 23, 37, 67, 101, 165, 265, 419, 691, 1123, 1789, 2909, 4657, 7515, 12183, 19657, 31635, 51101, 82449, 132989, 214623, 346485, 558587, 901399, 1454949, 2347157, 3787197, 6111131, 9858931, 15908393, 25669125, 41416849, 66826277

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OFFSET

0,4

LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..500

FORMULA

a(n) ~ c * d^n, where d = 1.61350953985228953675390530863679475666564394885974..., c = 0.5270561325668460003703909484716134447490733801644227... - Vaclav Kotesovec, Sep 21 2019

MAPLE

b:= proc(n, i, j) option remember; `if`(n=0, 1, add(

`if`(k=i or k=j, 0, (t-> b(t, `if`(k>t, 0, k),

`if`(i>t, 0, i)))(n-k)), k=1..n))

end:

a:= n-> b(n, 0$2):

seq(a(n), n=0..50);

MATHEMATICA

b[n_, i_, j_] := b[n, i, j] = If[n == 0, 1, Sum[If[k == i || k == j, 0, Function[t, b[t, If[k>t, 0, k], If[i>t, 0, i]]][n - k]], {k, 1, n}]];

a[n_] := b[n, 0, 0];

a /@ Range[0, 50] (* Jean-François Alcover, Dec 03 2020, after Alois P. Heinz *)

CROSSREFS